With the wide spread use of the Internet commercial transactions over the Internet have become commonplace. However, unlike commercial transactions that are conducted face-to-face, transactions over the Internet typically involve the exchange of private and confidential information, for example providing access to a party's bank account details, credit card details and home address.
Accordingly, many individuals still have concerns over confidentiality; as a result the full potential of the Internet is still not being utilized.
It is desirable to improve this situation.
Embodiments of the present invention to be described hereinafter make use of a cryptographic technology known as identifier-based encryption. Accordingly, a brief description will now be given of this type of encryption.
Identifier-Based Encryption (IBE) is an emerging cryptographic schema. In this schema (see FIG. 1 of the accompanying drawings), a data provider 10 encrypts payload data 13 using both an encryption key string 14, and public data 15 provided by a trusted authority 12. This public data 15 is derived by the trusted authority 12 using private data 17 and a one-way function 18. The data provider 10 then provides the encrypted payload data <13> to a recipient 11 who decrypts it, or has it decrypted, using a decryption key computed by the trusted authority 12 based on the encryption key string and its own private data.
A feature of identifier-based encryption is that because the decryption key is generated from the encryption key string, its generation can be postponed until needed for decryption.
Another feature of identifier-based encryption is that the encryption key string is cryptographically unconstrained and can be any kind of string, that is, any ordered series of bits whether derived from a character string, a serialized image bit map, a digitized sound signal, or any other data source. The string may be made up of more than one component and may be formed by data already subject to upstream processing. In order to avoid cryptographic attacks based on judicious selection of a key string to reveal information about the encryption process, as part of the encryption process the encryption key string is passed through a one-way function (typically some sort of hash function) thereby making it impossible to choose a cryptographically-prejudicial encryption key string. In applications where defence against such attacks is not important, it would be possible to omit this processing of the string.
Frequently, the encryption key string serves to “identify” the intended message recipient and this has given rise to the use of the label “identifier-based” or “identity-based” generally for cryptographic methods of the type under discussion. However, depending on the application to which such a cryptographic method is put, the string may serve a different purpose to that of identifying the intended recipient and, indeed, may be an arbitrary string having no other purpose than to form the basis of the cryptographic processes. Accordingly, the use of the term “identifier-based” or “IBE” herein in relation to cryptographic methods and systems is to be understood simply as implying that the methods and systems are based on the use of a cryptographically unconstrained string whether or not the string serves to identify the intended recipient. Generally, in the present specification, the term “encryption key string” or “EKS” is used rather than “identity string” or “identifier string”.
A number of IBE algorithms are known and FIG. 2 indicates, for three such algorithms, the following features, namely:                the form of the encryption parameters used, that is, the encryption key string and the public data of the trusted authority (TA);        the conversion process applied to the encryption key string to prevent attacks based on judicious selection of this string;        the primary encryption computation effected;        the form of the encrypted output.        
The three prior art IBE algorithms to which FIG. 2 relates are:                Quadratic Residuosity (QR) method as described in the paper: C. Cocks, “An identity based encryption scheme based on quadratic residues”, Proceedings of the 8th IMA International Conference on Cryptography and Coding, LNCS 2260, pp 360-363, Springer-Verlag, 2001. A brief description of this form of IBE is given hereinafter.        Bilinear Mappings p using, for example, a Tate pairing t or Weil pairing ê. Thus, for the Weil pairing:ê: G1×G1→G2 where G1 and G2 denote two algebraic groups of prime order q and G2 is a subgroup of a multiplicative group of a finite field. The Tate pairing can be similarly expressed though it is possible for it to be of asymmetric form:t: G1×G0→G2 where G0 is a further algebraic group the elements of which are not restricted to being of order q. Generally, the elements of the groups G0 and G1 are points on an elliptic curve though this is not necessarily the case. A description of this form of IBE method, using Weil pairings is given in the paper: D. Boneh, M. Franklin—“Identity-based Encryption from the Weil Pairing” in Advances in Cryptology—CRYPTO 2001, LNCS 2139, pp. 213-229, Springer-Verlag, 2001.        RSA-Based methods The RSA public key cryptographic method is well known and in its basic form is a two-party method in which a first party generates a public/private key pair and a second party uses the first party's public key to encrypt messages for sending to the first party, the latter then using its private key to decrypt the messages. A variant of the basic RSA method, known as “mediated RSA”, requires the involvement of a security mediator in order for a message recipient to be able to decrypt an encrypted message. An IBE method based on mediated RSA is described in the paper “Identity based encryption using mediated RSA”, D. Boneh, X. Ding and G. Tsudik, 3rd Workshop on Information Security Application, Jeju Island, Korea, August 2002.        
A more detailed description of the QR method is given below with reference to the entities depicted in FIG. 1 and using the same notation as given for this method in FIG. 2. In the QR method, the trusted authority's public data 15 comprises a value N that is a product of two random prime numbers p and q, where the values of p and q are the private data 17 of the trusted authority 12. The values of p and q should ideally be in the range of 2511 and 2512 and should both satisfy the equation: p,q≡3 mod 4. However, p and q must not have the same value. Also provided is a hash function # which when applied to a string returns a value in the range 0 to N−1.
Each bit of the user's payload data 13 is then encrypted as follows:                The data provider 10 generates random numbers t+ (where t+ is an integer in the range [0, 2N]) until a value of t+ is found that satisfies the equation jacobi(t+,N)=m′, where m′ has a value of −1 or 1 depending on whether the corresponding bit of the user's data is 0 or 1 respectively. (As is well known, the jacobi function is such that where x2≡#modN the jacobi (#, N)=−1 if x does not exist, and =1 if x does exist). The data provider 10 then computes the value:s+≡(t++K/t+)modN where: s+ corresponds to the encrypted value of the bit m′ concerned, andK=#(encryption key string)        Since K may be non-square, the data provider additionally generates additional random numbers t− (integers in the range [0, 2N)) until one is found that satisfies the equation jacobi(t−, N)=m′. The data provider 10 then computes the value:s−≡(t−−K/t)modN as the encrypted value of the bit m concerned.        
The encrypted values s+ and s− for each bit m′ of the user's data are then made available to the intended recipient 11, for example via e-mail or by being placed in a electronic public area; the identity of the trusted authority 12 and the encryption key string 14 will generally also be made available in the same way.
The encryption key string 14 is passed to the trusted authority 12 by any suitable means; for example, the recipient 11 may pass it to the trusted authority or some other route is used—indeed, the trusted authority may have initially provided the encryption key string. The trusted authority 12 determines the associated private key B by solving the equation:B2≡K modN (“positive” solution)
If a value of B does not exist, then there is a value of B that is satisfied by the equation:B2≡K modN (“negative” solution)
As N is a product of two prime numbers p, q it would be extremely difficult for any one to calculate the decryption key B with only knowledge of the encryption key string and N. However, as the trusted authority 12 has knowledge of p and q (i.e. two prime numbers) it is relatively straightforward for the trusted authority 12 to calculate B.
Any change to the encryption key string 14 will result in a decryption key 16 that will not decrypt the payload data 13 correctly. Therefore, the intended recipient 11 cannot alter the encryption key string before supplying it to the trusted authority 12.
The trusted authority 12 sends the decryption key to the data recipient 11 along with an indication of whether this is the “positive” or “negative” solution for B.
If the “positive” solution for the decryption key has been provided, the recipient 11 can now recover each bit m′ of the payload data 13 using:m′=jacobi (s++2B,N)
If the “negative” solution for the decryption key B has been provided, the recipient 11 recovers each bit m′ using:m′=jacobi (s−+2B,N)